Wow. That's going through a lot of gloves! Seriously, I would use your left hand to put and take out the negative from the developer and then the right with the fixer. It's those two baths that you really have to worry about. And then just rinse your gloved hand in between.
It seems to me the biggest issus is fix getting into the developer?

Sorry, I worked in a lab - the only way to know a glove is clean is to use a fresh one. I've just never counted on a rinsed glove to be free of chemicals. Yes, having fix on the glove and then touching an undeveloped sheet would cause that spot to not develop. Also, I use a kitchen LCD timer to time the chemicals and need a clean hand for that (also a lab holdover - I don't touch non-chemical things with a gloved hand). I may go farther than necessary, but that's like "over-engineering" - no such thing.